Linked bibliography for the SEP article "Frege’s Theorem and Foundations for Arithmetic" by Edward N. Zalta

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Primary Literature: Cited Works by Frege

  • 1879, Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle a. S.: Louis Nebert; translation by S. Bauer Mengelberg as Concept Notation: A formula language of pure thought, modelled upon that of arithmetic, in J. van Heijenoort, From Frege to Gödel: A Sourcebook in Mathematical Logic, 1879–1931, Cambridge, MA: Harvard University Press
  • 1884, Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl, Breslau: w. Koebner; translated by J. L. Austin as The Foundations of Arithmetic: A Logic-Mathematical Enquiry into the Concept of Number, Oxford: Blackwell, second revised edition, 1974.
  • 1892, “Über Begriff und Gegenstand”, in Vierteljahresschrift für wissenschaftliche Philosophie, 16: 192–205; translated as ‘Concept and Object,’ by P. Geach in Translations from the Philosophical Writings of Gottlob Frege, P. Geach and M. Black (eds. and trans.), Oxford: Blackwell, third edition, 1980. (Scholar)
  • 1893/1903, Grundgesetze der Arithmetik, Band I/II, Jena: Verlag Herman Pohle; translation by P. Ebert and M. Rossberg (with C. Wright) as Basic Laws of Arithmetic: Derived using concept-script, Oxford: Oxford University Press, 2013; partial translation of Volume I by M. Furth as The Basic Laws of Arithmetic, Berkeley: U. California Press, 1964. (Scholar)
  • 1967, The Basic Laws of Arithmetic, M. Furth (trans.), Berkeley: University of California.
  • 1974, The Foundations of Arithmetic, J. L. Austin (trans.), Oxford: Basil Blackwell.
  • 1980, Philosophical and Mathematical Correspondence, G. Gabriel, H. Hermes, F. Kambartel, C. Thiel, and A. Veraart (eds. of the German edition), abridged from the German edition by Brian McGuinness, translated by Hans Kaal, Chicago: University of Chicago Press.

Secondary Literature

  • Anderson, D., and Zalta, E., 2004, “Frege, Boolos, and Logical Objects”, J. Philosophical Logic, 33 (1): 1–26. (Scholar)
  • Antonelli, A., and May, R., 2005, “Frege’s Other Program”, Notre Dame Journal of Formal Logic, 46 (1): 1–17. [Available online in PDF.] (Scholar)
  • Beaney, M., 1997, The Frege Reader, Oxford: Blackwell. (Scholar)
  • Bell, J. L., 1995, “Type-Reducing Correspondences and Well-Orderings: Frege’s and Zermelo’s Construction Re-examined”, Journal of Symbolic Logic, 60: 209–221. (Scholar)
  • –––, 1999, “Frege’s Theorem in a Constructive Setting”, Journal of Symbolic Logic, 64 (2): 486–488. (Scholar)
  • –––, 1994, “Fregean Extensions of First-Order Theories”, Mathematical Logic Quarterly, 40: 27–30; reprinted in Demopoulos 1995, 432–437. (Scholar)
  • Boolos, G., 1985, “Reading the Begriffsschrift”, Mind, 94: 331–344; reprinted in Boolos (1998): 155–170. [Page references are to the reprint.] (Scholar)
  • –––, 1986, “Saving Frege From Contradiction”, in Proceedings of the Aristotelian Society, 87 (1986/1987): 137–151; reprinted in Boolos (1998): 171–182. [Page references are to the original.] (Scholar)
  • –––, 1987, “The Consistency of Frege’s Foundations of Arithmetic”, in On Being and Saying, J. J. Thomson (ed.), Cambridge, MA: MIT Press, pp. 3–20; reprinted in Boolos (1998): 183–201. [Page references are to the original.] (Scholar)
  • –––, 1990, “The Standard of Equality of Numbers”, in Meaning and Method: Essays in Honor of Hilary Putnam, G. Boolos (ed.), Cambridge: Cambridge University Press, pp. 261–277; reprinted in Boolos (1998): 202–219. [Page references are to the original.] (Scholar)
  • –––, 1993, “Whence the Contradiction?”, in Aristotelian Society Supplementary Volume, 67: 213–233; reprinted in Boolos (1998): 220–236. (Scholar)
  • –––, 1994, “The Advantages of Honest Toil Over Theft”, in Mathematics and Mind, Alexander George (ed.), Oxford: Oxford University Press, 27–44; reprinted in Boolos (1998): 255–274. (Scholar)
  • –––, 1997, “Is Hume’s Principle Analytic?”, in Heck (ed.) 1997, 245–262; reprinted in Boolos (1998): 301–314. [Page references are to the reprint.] (Scholar)
  • –––, 1998, Logic, Logic, and Logic, J. Burgess and R. Jeffrey (eds.), Cambridge, MA: Harvard University Press. (Scholar)
  • Burgess, J., 1984, “Review of Wright (1983)”, The Philosophical Review, 93: 638–40. (Scholar)
  • –––, 1998, “On a Consistent Subsystem of Frege’s Grundgesetze”, Notre Dame Journal of Formal Logic, 39: 274–278. (Scholar)
  • –––, 2005, Fixing Frege, Princeton: Princeton University Press. (Scholar)
  • Demopoulos, W., 1998, “The Philosophical Basis of Our Knowledge of Number”, Noûs, 32: 481–503. (Scholar)
  • Demopoulos, W., (ed.), 1995, Frege’s Philosophy of Mathematics, Cambridge: Harvard University Press. (Scholar)
  • Demopoulos, W., and Clark, P., 2005, “The Logicism of Frege, Dedekind and Russell”, in Oxford Handbook of Philosophy of Mathematics and Logic, S. Shapiro (ed.), Oxford: Oxford University Press, 129–165. (Scholar)
  • Dummett, M., 1991, Frege: Philosophy of Mathematics, Cambridge: Harvard University Press. (Scholar)
  • –––, 1997, “Neo-Fregeans: In Bad Company?”, in Schirn (1997). (Scholar)
  • Ferreira, F., 2005, “Amending Frege’s Grundgesetze der Arithmetik”, Synthese, 147: 3–19. (Scholar)
  • Ferreira, F., and K. Wehmeier, 2002, “On the Consistency of the \(\Delta^1_1\)-CA Fragment of Frege’s Grundgesetze”, Journal of Philosophical Logic, 31: 303–311. (Scholar)
  • Field, H., 1984, “Critical Notice of Crispin Wright: Frege’s Conception of Numbers as Objects”, Canadian Journal of Philosophy, 14: 637–632; reprinted under the title “Platonism for Cheap? Crispin Wright on Frege’s Context Principle” in H. Field, Realism, Mathematics, and Modality, Oxford: Blackwell, 1989, pp. 147–170. (Scholar)
  • Fine, K., 2002, The Limits of Abstraction, Oxford: Clarendon Press. (Scholar)
  • Furth, M., 1967, “Editor’s Introduction”, in G. Frege, The Basic Laws of Arithmetic, M. Furth (translator and editor), Berkeley: University of California Press, pp. v–lvii. (Scholar)
  • Geach, P., 1976, “Critical Notice”, Mind, 85 (339): 436–449. (Scholar)
  • –––, 1955, “Class and Concept”, Philosophical Review, 64: 561–570. (Scholar)
  • Goldfarb, W., 2001, “First-Order Frege Theory is Undecidable”, Journal of Philosophical Logic, 30: 613–616. (Scholar)
  • Hale, B., 1994, “Dummett’s Critique of Wright’s Attempt to Resuscitate Frege”, Philosophia Mathematica, (Series III), 2: 122–147. (Scholar)
  • Hazen, A., 1985, “Review of Crispin Wright’s Frege’s Conception of Numbers as Objects”, Australasian Journal of Philosophy, 63 (2): 251–254. (Scholar)
  • Heck, Jr., R., 2012, Reading Frege’s Grundgesetze, Oxford: Clarendon Press. (Scholar)
  • –––, 2011, Frege’s Theorem, Oxford: Clarendon Press. (Scholar)
  • –––, 1999, “Grundgesetze der Arithmetik I, §10”, Philosophia Mathematica, 7: 258–292. (Scholar)
  • –––, 1997, “The Julius Caesar Objection”, in Heck (ed.) 1997, 273–308. (Scholar)
  • –––, 1996, “The Consistency of Predicative Fragments of Frege’s Grundgesetze der Arithmetik”, History and Philosophy of Logic, 17: 209–220. (Scholar)
  • –––, 1993, “The Development of Arithmetic in Frege’s Grundgesetze der Arithmetik”, Journal of Symbolic Logic, 58 (2): 579–600; reprinted in Demopoulos (1995). (Scholar)
  • Heck, R. (ed.), 1997, Language, Thought, and Logic: Essays in Honour of Michael Dummett, Oxford: Oxford University Press, 1997. (Scholar)
  • Hodes, H., 1984, “Logicism and the Ontological Commitments of Arithmetic,” Journal of Philosophy, 81 (3): 123–149. (Scholar)
  • Linnebo, Ø., 2004, “Predicative Fragments of Frege Arithmetic”, The Bulletin of Symbolic Logic, 10 (2): 153–174. (Scholar)
  • MacBride, F., 2003, “Speaking with Shadows: A Study of Neo-Logicism”, British Journal for the Philosophy of Science, 54: 103–163. (Scholar)
  • MacFarlane, J., 2002, “Frege, Kant, and the Logic in Logicism”, The Philosophical Review,111:25–65. (Scholar)
  • May, R., and K. Wehmeier, forthcoming, “The Proof of Hume’ Principle”, P. Ebert and M. Rossberg (eds.), A Companion to Frege’s Grundgesetze, Oxford: Oxford University Press. (Scholar)
  • Parsons, C., 1965, “Frege’s Theory of Number”, Philosophy in America, M. Black (ed.), Ithaca: Cornell University Press, pp. 180–203; reprinted with Postscript in Demopoulos (1995), pp. 182–210. (Scholar)
  • Parsons, T., 1987, “The Consistency of the First-Order Portion of Frege’s Logical System”, Notre Dame Journal of Formal Logic, 28: 161–68. (Scholar)
  • Pelletier, F.J., 2001, “Did Frege Believe Frege’s Principle”, Journal of Logic, Language, and Information, 10 (1): 87–114. (Scholar)
  • Quine, W.V.O., 1995, “On Frege’s Way Out”, in Selected Logical Papers (enlarged edition), Cambridge, MA: Harvard University Press. (Scholar)
  • Reck, E., and Awodey, S. (trans./eds.), 2004, Frege’s Lectures on Logic: Carnap’s Student Notes, 1910–1914, Chicago and La Salle, IL: Open Court. (Scholar)
  • Resnik, M., 1980, Frege and the Philosophy of Mathematics, Ithaca: Cornell University Press. (Scholar)
  • Rosen, G., 1993, “The Refutation of Nominalism(?)”, Philosophical Topics, 21 (2): 149–186 (Scholar)
  • Ruffino, M., 2003, “Why Frege Would Not Be A Neo-Fregean”, Mind, 112 (445): 51–78. (Scholar)
  • Schirn, M., (ed.), 1997, Philosophy of Mathematics Today, Oxford: Oxford University Press. (Scholar)
  • Schroeder-Heister, P., 1987, “A model-theoretic reconstruction of Frege’s Permutation Argument”, Notre Dame Journal of Formal Logic, 28 (1): 69–79. (Scholar)
  • Sullivan, P. and Potter, M., 1997, “Hale on Caesar”, Philosophia Mathematica (Series III), 5: 135–152. (Scholar)
  • Tabata, H., 2000, “Frege’s Theorem and His Logicism”, History and Philosophy of Logic, 21 (4): 265–295. (Scholar)
  • Tennant, N., 2004, “A General Theory of Abstraction Operators”, The Philosophical Quarterly, 54(214): 105–133. (Scholar)
  • van Heijenoort, J., 1967, ed., From Frege to Gödel: A Sourcebook in Mathematical Logic, Cambridge: Harvard University Press.
  • Wehmeier, K., 1999, “Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects”, Synthese, 121: 309–328. (Scholar)
  • Whitehead, A. N. and Russell, B., 1912, Principia Mathematica Vol. II, Cambridge: Cambridge University Press. (Scholar)
  • Wright, C., 1983, Frege’s Conception of Numbers as Objects, Aberdeen: Aberdeen University Press. (Scholar)
  • –––, 1997a, “Response to Dummett”, in Schirn (1997). (Scholar)
  • –––, 1997b, “On the Philosophical Significance of Frege’s Theorem”, in Heck (ed.) 1997, 201–244. (Scholar)
  • Zalta, E., 1999, “Natural Numbers and Natural Cardinals as Abstract Objects: A Partial Reconstruction of Frege’s Grundgesetze in Object Theory”, Journal of Philosophical Logic, 28 (6): 619–660. (Scholar)

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